Derivatives of Inverse Functions | Calculus

This calculus video tutorial provides a basic introduction into the derivatives of inverse functions. It explains how to evaluate the derivative of an inverse function at a point using a simple formula.
Derivatives - Fast Review: • Calculus 1 - Derivatives
Derivatives - The Product Rule - f*g:
• Product Rule For Deriv...
Derivatives - The Quotient Rule:
• Quotient Rule For Deri...
Derivatives - The Chain Rule:
• Chain Rule For Finding...
Derivatives - Composite Functions:
• Derivatives of Composi...
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Implicit Differentiation:
• Implicit Differentiation
Derivatives of Inverse Trig Functions:
• Derivatives of Inverse...
Derivatives of Exponential Functions:
• Derivatives of Exponen...
Derivatives of Logarithmic Functions:
• Derivative of Logarith...
Logarithmic Differentiation:
• Introduction to Logari...
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Derivatives - Using Logarithms:
• Finding Derivatives Us...
Derivatives of Inverse Functions:
• Derivatives of Inverse...
Derivatives - Differentiation Rules:
• Basic Differentiation ...
Derivatives - Function Notations:
• dy/dx, d/dx, and dy/dt...
Derivatives - The Reciprocal Rule:
• The Reciprocal Rule an...
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/f6evoYFnfJaBmck Final Exams and Video Playlists: www.video-tutor.net/

[@harisahmad7871]

if you find x2 and y2 very confusing, just do this: 1) Write the equation 2) Substitute f(x) with y 3) Substitute y with x and x with y 4) Solve for y 5) Replace y with f^-1(x) 6) Take the derivative 7) Finally, replace x with the given number Ex: 1) f(x) = x^3 + 3, [f^-1(11)]' 2) y = x^3 + 3 3) x = y^3 + 3 4) y = (3)square root of (x-3) 5) f^-1(x) = (3)square root of (x-3) f^-1(x) = (x-3)^(1/3) 6) f^(-1)'(x) = 1 / [3(x-3)^2/3] 7) f^(-1)'(x) = 1 / [3(11-3)^2/3] f^(-1)'(x) = 12

[@sidindian1982]

You made my Day Sir 🙂

[@riskygadget4life]

Its 1/12

[@jerrysterling4432]

Finally... It clicked. This whole approach with tracking the X1 Y1, X2 Y2 saved my shit man. Hell yeah.

[@joehoe5770]

I love your channel. Oddly, i can't believe how much i miss its simplicity, its sentiments and the sheer intelligence it takes to understand it ..ur awesome

[@ilovebutter9563]

thx for your generous help I'm gonna cry...

[@cefb8923]

Just remember its a wash out course lol. Keep that in mind.

[@Oschar157]

@@cefb8923 whats that mean

[@peterk.2108]

@@Oschar157I’m guessing he means weed out, which means it’s a course that many people drop because it’s hard to

[@faleeba7494]

You are literally getting me through my calculus course thank you so much!!!

[@petertran5419]

Best explanation in the web that I can find so far. Nice.

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a solid analysis of the Derivatives of Inverse Functions in Calculus Two. This is one topic in Calculus that I do not understand from start to finish. I will rewatch this video and do problems in order to understand this material. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@Maricookieme]

my university professor couldn't explain this subject as well as you did, THANK YOU!

[@ueda6512]

Amazing video, clear as the water of a swiss river in spring!

[@AhmetOmerOzgen]

this one is a bit complicated but works like a charm.

[@_-_-_-_-_-_-_-__-]

Helps a crap ton, thank you so much.

[@mohammadzaid4100]

God bless this channel Love u man👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻💋💋

[@wandamilliman2763]

Finding the derivative of the inverse has always been a struggle. Keep it simple, is my recommendation. The derivative of the inverse is 1 divided by the derivative of the function at the y value of the x value given. I would like to see more derivatives of inverses without the specific value, but just the function of the inverse's derivative.

[@1grace]

This is so clear!

[@almouyad8838]

Finally, I found a person like me 🙂

[@vedantsawant3295]

U helped me so muchhh thanks

[@anthonyfigueroaa7024]

thank you

[@madbggyhat]

Yo teach you dropped your crown 👑

[@zakiahr7379]

you are amazing

[@Maybec]

gracias amigo

[@rosskious7084]

At 5:14 you switched y and x , but did not solve for the inverse. I guess this means just switching the variables and doing implicit differentiation give you the equation for the slo P of the inverse?

[@irvingsandoval617]

great video

[@shadinmuraysh]

You are an angel sent from heaven thank you

[@user-yj5dn2pf3k]

thank you.

[@rosanaalfaro2921]

Beautiful

[@faridgulum1226]

I do not understand why he did not plug-in 3 after finding derivation of the function f'(3). Instead he found (x1,y1) (x2,y2) separately and plugged in 1.

[@mahmoudezzat5460]

thankk youuu

[@chriswilliams5291]

8 minutes 40 seconds. You mention a leading coefficient test of the constant term and leading coefficient making the factors plus minus 1 and plus minus 5. Would factoring it to be (x+5)(x-1) = 0 be an incorrect method? I plugged in x =1 with this method and found it to be = 0.

[@kataxiro]

I’m totally gonna pass my exam on Friday 😏

[@murtuzalemonwala4605]

How is f inverse of x equal to y2? 2:04

[@lololol559]

F(x2) = y1 F-1(x2) = y2

[@hibamerci1953]

at 04:18 where did the 3x^2 come from? someone please help

[@harvir6167]

that's the derivative of x^3 + 3, using the power rule. He's taking the derivative of the equation above. The little 1 looking symbol next to f is called prime, which means taking derivative of the function f.

[@hibamerci1953]

+Harvir aha now I got it thank you.

[@MrVsteel]

The Derivative of a cubic function is a quadratic, and so on...

[@geraldcifuni1344]

You made the derivative of the inverse function much more complex than it really is. You were too technical for a struggling AP student to comprehend. I appreciate the various methods you applied to obtain an answer. Unfortunately, many students might become overwhelmed with the excess information that you displayed in your video. For the above-average AP students, your video is awesome. Yet for the average student, it might be too challenging to digest. To all AP students who need help with this concept view Alaina Vasta video. It is on KZbin. I guarantee you that after watching her video you will have no problems solving this type of problem on the AP Calculus Exam.

[@MikiyasMogess]

❤

[@whunderwhoiam2489]

I literally can't keep track of all these numbers.... thats why i suck at inverses.

[@rosanaalfaro2921]

WHY DOES MY TEXTBOOK MAKE IT SOUND SO COMPLICATED THEN

[@antoinecharlesdegaulle580]

no idea it always does

[@abdullahh.mesawa5206]

i love you

[@markjaysalayo8376]

I think you have a wrong answer it should be 1/24 not 1/12 just my opinion hahah because you forgot to times the 12 in 2

[@arisoda]

5:21 HOW CAN THIS BE THE INVERSE FUNCTION when the inverse function is actually (x-3)^1/3 ???? You've only switched x and y, but haven't actually done any inversion ?!?!?!

[@karatekid8312]

it's literally the same thing!!

[@arisoda]

@@karatekid8312 no it's not! Changing the variables doesn't mean it's the inverse, you actually have to swap it using algebra. I mean, what else does this supposed to mean: (x-3)^1/3 ? Just like the inverse of x^2 is x^1/2 RIGHT?

[@AlexVoxel]

This is not a tutorial, it's you making exercises, we need more explanation!

[@bernaibrahimli7427]

stfu

[@nightbot.2341]

Ur just stupid

[@midgette_201]

He explains the process during the problems

[@DawitMan-wo7mp]

❤